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The following generalizations of the Chacon map are proposed: instead ofclassical constant spacer sequence $(0,1,0)$ let a sequence $(0,s_j,0)$ be onewith unbounded $s_j$. (We mention also an analogue of the historical Chacon mapwith spacer sequences in the form $(0,s_j)$.) This narrow class of rank-onetransformations may be abundant source of open questions. All suchconstructions have partial rigidity, but some other properties could bedifferent. For root sequence, $ s_j= [\sqrt{j}]$, (or $ s_j= [\ln{j}]$) thecorresponding action is rigid, moreover it possesses all polynomials in itsweak closure. In the linear case $s_j={j}$ we get (as well as for the classicalChacon transformation) the property of minimal self-joinings (MSJ). We presentsome observations about MSJ, mild mixing, partial mixing, $\ae$-mixing, absenceof factors, triviality of centralizer and spectral primality, state severalproblems, and mention exponential "self-similar" Chacon transformations andflows on infinite measure spaces.

Chacon's Type Ergodic Transformations with Unbounded Arithmetic Spacers